Question

The probability that it will rain today is 0.5. The probability that it will rain tomorrow is 0.6. The probability that it will rain either today or tomorrow is 0.7. What is the probability that it will rain today and tomorrow?

• A. 0.3
• B. 0.25
• C. 0.35
• D. 0.4

Answer 1

The correct option is A 0.3

$$GivenP\left(E_1\right)=0.5,P\left(E_2\right)=0.6$$
& $P(E_1\cup E_2)=0.7$

$P(E_1\cup E_2)=P\left(E_1\right)+P\left(E_2\right)-P(E_1\cap E_2)$

$0.7=0.5+0.6-P(E_1\cap E_2)$

$P(E_1\cap E_2)=0.4$